The political history of Equestria can be hinted at in the episodes Hearth's Warming Eve and Princess Spike as well as the book The Journal of the Two Sisters. It was probably Star Swirl the Bearded that got the three tribes of Earth ponies, Unicorns, and Pegasi to unite under royal rule of Alicorns Princess Celestia and Princess Luna.
The Equestrian monarchy was at first a joint monarchy or coregency (rule by two sovereigns).
After Princess Luna was banished to the moon for one thousand years after being defeated by her sister Celestia, Princess Celestia during these centuries probably summoned local representatives periodically from local pony communities across Equestria to help her govern her kingdom. In other words, the beginning of the occasional Grand Equestria Pony Summit as a permanent political institution (much like the rise of Parliament in pre-UK England).
Princess Celestia probably appointed Princess Cadance a couple of years before the return of her sister Luna in order to restore the Equestrian monarchy as a coregency.
With the return of Princess Luna and the promotion of Twilight Sparkle to an Alicorn Princess has further strengthened the pony monarchy as a coregency (are Cadance and Twilight being groomed to eventually replace Celestia and Luna when they finally die?).
By the period of time covered by the TV series My Little Pony Friendship is Magic, it had become unwritten convention that the ruling Princess or Princesses not issue Royal decrees without consulting delegates to the Grand Equestrian Pony Summit.
The Status of the Crystal Empire Within Equestria
The kingdom of the Crystal Ponies was probably founded under the leadership of Princess Amore independently of Equestria. However, with the rise of the cruel King Sombra, Princesses Celestia and Luna after defeating Sombra officially annexed the Crystal Pony kingdom as a locally autonomous province of Equestria. Sombra's curse made the Crystal Empire disappear for a thousand years. With the reappearance of the Crystal Ponies' kingdom and the second defeat of Sombra, Equestria again annexed the Crystal Empire with local autonomy for the Crystal Ponies, of course. Princess Cadance and her husband Shining Armor rule the Crystal Ponies as a joint monarchy or coregency. They also probably summon local representatives to a Crystal Pony Summit modeled after the Grand Equestrian Pony Summit.
The Grand Equestrian Pony Summit will likely evolve into a full-fledged parliament with true legislative and executive powers, although the ruling Alicorn princesses will still preside over meetings of the GEPS and theoretically still have veto power over Summit legislation (although in practice the royal assent will almost always be granted to proposals passed by the Summit.